On the Generation of Rational Function Approximations for Laplace Transform Inversion with an Application to Viscoelasticity

From the Maclaurin expansion of a function f( p ) of the Laplace transform operator p, rational function approximations to f( p ) are generated by means of a new nonlinear sequence to sequence transformation due to Levin. These rational functions are then inverted analytically to yield a sequence of approximations fₙ ( t ) to the inverse $f( t )$ of f( p ). In a simple example, these approximations are shown to be superior to those obtained from comparable elements of the Padé table of f( p ). A subroutine for generating these approximations is given in the Appendix. An application to an important problem in viscoelasticity is presented, and here again the superiority over the Padé approximations is evident.